Question

A fair die will be rolled 11 times. what is the probability that 1, 2, or 3 is rolled exactly 4 times? round your answer to four decimal places.

Answer 1

1/11. Because you divide and then bring to simpilist form

Answer 2

The probability of a 1, 2, or 3 is 3/6 = 1/2. There are C(11,4) = 11!/(4!(11-4)!) = 330 ways the desired outcome can show up in the 11 rolls. The probability is

... 330×(1/2)⁴(1/2)⁷ = 330/2048 ≈ 0.1611